Acknowledgement. We thank Science for their permission to use an excerpt from:
Tyler, G. L., et al. 1981. Radio Science Investigations of the Saturn System with Voyager 1:Preliminary Results. Science 212 (4491), 201-206. (Excerpt from pp. 203-205.)
Saturn's rings. Voyager 1 emerged from behind Saturn at approximately 2 degrees S, within the eastern ansa of the rings as seen from Earth. The spacecraft was then successively occulted by the C, B, and A rings, so that the radio path between the spacecraft and Earth was transected in order by these features. The received signals consisted of the attenuated energy propagating along the direct ray between Voyager 1 and Earth, and a second component scattered in the near-forward direction by particles within the extended beam of the spacecraft antenna (18). Thus the oblique optical depth of a point in the rings and the forward-scattering cross section of the surrounding region could be observed simultaneously. In addition, the Voyager 1 trajectory was chosen in part to produce a close alignment, within the region illuminated by Voyager 1, between the contours of constant received Doppler frequency and individual ringlets within the ring system (19), permitting ready mapping of the scattering phase function of any identifiable ring feature.
The preliminary data consist of a sequence of power-frequency spectra from the real-time monitor, which represent the region surrounding the received 3.6 cm wavelength data. These spectra have about 40 degrees of freedom and represent a few seconds of incoherent integration (20). The dynamic range of observation was about 40 dB for the direct signal, which could be identified as a coherent line in the monitor spectra.
We can measure simultaneously the attenuation of the direct signal and the strength of the near-forward-scattered energy during periods when the spacecraft was behind the A and C rings and the Cassini division. The attenuation of the B ring exceeds the dynamic range of the real-time monitor; neither direct nor scattered signal was detected for this feature (21). We can also identify and measure the near-forward-scattering phase function for the outer third of the Cassini division, based on the Doppler mapping mentioned above (1, 22).
Table 1 (23) presents estimates of the particle size in Saturn's rings from observations of the optical depth and scattering gain at the 3.6-cm wavelength. The values of particle size refer to the effective or "equivalent" scattering size, that is, the particle diameter in a monodispersive size distribution that would produce the combination of direct signal loss and forward-scattered power observed. The simplest model consistent with the 3.6 cm observation above is one in which all particles in each feature are the size given in Table 1. In the case of the Cassini division, the diffraction lobe of the scatter is apparent in the data (24); the width of this lobe is consistent with the size obtained from the combination of optical depth and scattering cross section. Note that our results for particle size apply only to limited regions of the rings and not to the system as a whole.
In Table 1, the optical depths of the A and C rings are in rough agreement with traditional values, but the optical depth of the Cassini division is larger than expected. The particle sizes are consistent with either a narrow distribution of large particles of about the size given, or a broad distribution of sizes such as might result from collisional processes (25). In either case, the 10-m size is larger than or at the upper limit of sizes usually stated in the observational literature.
With regard to distributions of sizes inferred from radar observations, the contribution of each particle to the backscatter cross section is weighted as D^2, where D is the diameter, assumed to be larger than or comparable to lambda/3, where lambda is the wavelength. For forward scatter the weighting is D^4. Thus, for example, scattering particles with an inverse-cube-law size distribution would be inversely weighted with respect to size for scattering in the forward and back directions; the largest particles would contribute heavily to forward scatter, while the smallest particles would be most important in backscatter. Recent estimates of particles in the size range 2 to 200 cm based on radar backscatter and microwave emissions (26) are consistent with our results if one assumes a distribution similar to an inverse cube law.
Additional information about the particle size distribution is contained in the wavelength dependence of the optical depth and in the forward-scattering phase diagram of the ring particles. A thorough study of the particle size distribution must await the reduction of the complete ring occultation data set.
Last updated Feb-27-1997
